Resumen de Existence of Solutions of a Superlinear Elliptic System at Resonance

Ruyun Ma, Mantang Ma, Yan Zhu

• We are concerned with the existence of solution for elliptic system ⎧⎩⎨⎪⎪−Δu=λu+δv+f(u+)+k1(x)−Δv=δu+γv+g(v+)+k2(x)u=v=0in Ω,in Ω,on ∂Ω, where Ω⊂RN , N≥3 , is a smooth bounded domain, s+:=max{s,0} , λ,δ and γ are real parameters such that max{λ,γ}>0 and δ>0 . By topological degree arguments, we show the existence of nontrivial solutions for above system under certain superlinear growth conditions on f, g and an one-sided Landesman−Lazer condition on k1,k2 . Also, a priori bound for the solutions are obtained by adapting the method of Brezis−Turner.